Using GIS to measure from maps: Aggregating data
Chapter 4: Mapping Crime and Geographic Information Systems

Why measure? In the most general sense, measurement is the foundation of scientific analysis, and it lies behind any quantitative analytical statement. For example, what is the crime rate? To answer this we have to know the base of the rate. Do we want it per 1,000 persons, per reporting area, or per patrol district? To calculate this rate we must know how many crime incidents have occurred, and, if we are calculating a population-based rate, how many persons there are per unit area. This value, the base of our rate, is also known as the denominator, because it is the bottom of the fraction used to calculate the rate. Therefore:

density =  number of incidents per area

population per area

Here, "number of incidents per area" is the numerator (top of the fraction) and "population per area" is the denominator. If there are 428 incidents and the population expressed in thousands is 3.7, the rate is 428/3.7, or 115.68 per 1,000 persons. We can check that the calculation is correct by multiplying the rate by the population to reproduce the original incident count:

115.68 x 3.7 = 428.

A GIS program would do these calculations for you, but analysts need to know how to provide appropriate instructions before anything useful can be produced.

An application of density analysis is shown in figures 4.11, 4.12, and 4.13. First, the density of burglar alarm calls was mapped using 48,622 locations for alarm calls in 1990 in Charlotte-Mecklenburg, North Carolina. Using the ArcView Spatial Analyst extension, a grid was used to generate the surface shown in figure 4.11. Peaks occurred near the central business district, along major transportation arteries, and in the industrial northwest area. A similar map (see figure 4.12) was prepared to show the density of the 10,288 burglaries reported in 1990, focusing on both the central business district and a radial, highway-oriented distribution. In the final phase, the burglary density surface was subtracted from the alarm density surface, and a query tool was used to select parts of the surface where burglary density exceeded alarm call density (see figure 4.13). This map directs the analyst to areas where displacement may be occurring and suggests areas for possible interventions. Such interventions could include additional alarm installations or other target hardening measures.

Figure 4.11

Figure 4.12

Figure 4.13

The various types of measurement now available in GIS programs are too numerous to describe. However, a few types of measurement will be outlined to provide a sense of what can be done.

Count incidents in areas

Although the primary need for counting will be to total crime incidents, counting other objects or events could be useful, too. It may be helpful, for example, to know how many and what types of alcoholic beverage licenses (beer, liquor, restaurant, liquor store, and so forth) are in specific areas. The information could serve as a gross index of alcohol availability, although it would not necessarily indicate where or how much alcohol is consumed or by whom. Or perhaps the local building inspection agency supplies a list of addresses of code violations. These could be mapped and sorted by any relevant areas, such as neighborhood association jurisdictions or police operations areas. GIS software makes such identification easy. Users may find it helpful to write down the operation they want to do to clarify the steps-especially if they anticipate several steps of filtering, measuring, or other manipulations. In fact, this exercise is helpful for any kind of analysis. For example, you might want to count incidents of spousal abuse within patrol districts, which in some programs might be expressed in SQL something like this:

count spousal abuse.object
within patrol district.object

This tells the program to evaluate each spousal abuse incident ("object") and determine in which patrol district it occurred. Additional instructions may ask the program to group incidents by patrol district by listing in a new table or file each patrol district identification number and the number of spousal abuse incidents that occurred there.

Measure areas and distances

Area measurements are especially useful for determining how many crimes occur per unit area. This is not to be confused with crime measurements by population size or density. Generally, though not necessarily, crime densities will reflect population densities because population density is an expression of crime potential. More people means more potential victims and offenders.

Distance measurements are also simple. They require the use of ruler or tape software tools and, as with area measurements, the units can easily be changed.

Measure inclusion and overlap

Areas of interest in policing do not always fit together neatly. Police districts, precincts, patrol areas, and so forth, may not match school districts, council districts, census tracts, neighborhoods, community conservation districts, and officially designated hot spots. GIS tools allow users to measure overlaps between areas or small enclaves in large areas because any incidents found in a specific area can be electronically identified. All the crimes (or drug markets, liquor licenses, parolee addresses, injury accidents, and so forth) in a specific area can be selected and separated as a new data set for special analysis. How are drug arrests divided among council districts or neighborhood association areas? One GIS package, for example, includes the following functions: contains, contains entire, within, entirely within, intersects. These capabilities are typical of this type of analytical function.

Centroid display

A centroid is an area's center defined as the halfway point on its east-west and north-south boundaries. However, the centroid will not always be inside the area. For example, an area may be L-shaped, in which case the centroid theoretically would fall outside the area. A centroid is generally used as the point where labels will be located by default and where statistical symbols will be placed.

Centroids can approximate the geographic midpoints of areas, which may in turn (theoretically) approximate the most accessible points in the areas. Normally, centroids are hidden, but they can be displayed on request. If you have area objects without centroids, the centroid (x,y) function can be used to generate them. Centroids are used infrequently in crime analysis and are typically used as surrogates for other conditions, such as accessibility.

For surface-fitting purposes, the data values that apply to tracts, block groups, or blocks could be assigned to their centroids, thus reducing areas to points for computational convenience. Given the common use of grid-based, surface-fitting algorithms, however, this type of centroid application is unlikely.

Chapter 4: Mapping Crime and Geographic Information Systems
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Mapping Crime: Principle and Practice, by Keith Harries, Ph.D., December 1999